We have recast the problem of t ru th maintenance in a setting of algebraic equations over Boolean lattices. If a method of labeling propositions to justi fy them according to some reasoning agent's constraints of belief happens to conform to the postulates of Boolean lattices, the labeling system can be reformulated as an algebraic equation solving system. A l l t ru th maintenance systems kno...

In this paper we consider the supervisory control problem through language equation solving. The equation solving approach allows to deal with more general topologies and to find a largest supervisor which can be used as a reservoir for deriving an optimal controller. We introduce the notions of solutions under partial controllability and partial observability, and we show how supervisory contr...

Zhi-Gang Wang , Wei-Min Yang and Shao-Long Wan 1 Department of Physics, North China Electric Power University, Baoding 071003, P. R. China † 2 CCAST (World Laboratory), P.O.Box 8730, Beijing 100080, P. R. China 3 Department of Modern Physics, University of Science and Technology of China, Hefei 230026, P. R. China In this article, we investigate the structures of the pseudoscalar mesons (π, K, ...

The purpose of this paper is to study the influence of large or unbounded domains on a stochastic PDE near a change of stability, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider the stochastic Swift-Hohenberg equation and derive rigorously the Ginzburg-Landau equation as a modulation equation for the amplitudes of...

We discuss the use of the formal theory of differential equations in the numerical analysis of general systems of partial differential equations. This theory provides us with a very powerful and natural framework for generalising many ideas from differential algebraic equations to partial differential equations. We study in particular the existence and uniqueness of (formal) solutions, the meth...

In this work, we construct the general solution to the Heat Equation (HE) and to many tensor structures associated to the Heat Equation, such as Symmetries, Lagrangians, Poisson Brackets (PB) and Lagrange Brackets (LB), using newly devised techniques that may be applied to any linear equation (e.g., Schrödinger Equation in field theory, or the small-oscillations problem in mechanics). In partic...